**Surfaces and Topology**

If we count the number of vertices, v, on a cube, v = 8, number of edges e = 12, and number of faces f = 6, then v¬ – e + f = 2. The same is true for a tetrahedron where v¬ = 4, e = 6 and f = 4. In fact, the mathematician Leonhard Euler obtained the amazing result that v¬ – e + f = 2 for a wide class of polyhedrons. This theorem of Euler is a result in topology, a subject which tries to find those properties of geometrical objects that are invariant under continuous deformation – a tetrahedron can be changed in this way into a cube. Topology is sometimes called rubber sheet geometry.

Raymond Flood has spent most of his academic life promoting mathematics and computing to adult audiences, mainly through his position as University Lecturer at Oxford University, in the Continuing Education Department and at Kellogg College. In parallel he has worked extensively on the history of mathematics, producing many books and writing diverse educational material.

He is Emeritus Fellow of Kellogg College, Oxford, having been Vice-President of the College and President of the British Society for the History of Mathematics before retiring in 2010. He is a graduate of Queen’s University, Belfast; Linacre College, Oxford; and University College, Dublin where he obtained his PhD.

He enjoys communicating mathematics and its history to non-specialist audiences, as he has done recently on BBC Radio 4’s *In Our Time* and on transatlantic voyages with the QM2. Two of the most recent books with which he has been involved are *The Great Mathematicians, *which celebrates the achievements of the great mathematicians in their historical context, and *Mathematics in Victorian Britain*,which assembles into a single resource research on the history of mathematicians that would otherwise be out of reach of the general reader.

His first year of lectures as Gresham Professor of Geometry was titled *Shaping Modern Mathematics*:

The 19^{th} Century saw the development of a mathematics profession with people earning their living from teaching, examining and researching and with the mathematical centre of gravity moving from France to Germany. A lot of the mathematics taught at university today was initiated at that time. Whereas in the 18^{th} Century one would use the term *mathematician*, by the end of the 19^{th} Century one had specialists in *analysis, algebra, geometry, number theory, probability* *and statistics*, and *applied mathematics*. This series of free public lectures looks at the shaping of each of these mathematical areas and at the people who were involved.

Professor Flood continues his Geometry series in the 2015/16 academic year, entitled 'Great Mathematicians, Great Mathematics'.

Professor Flood's previous lecture series' are as follows:

2014/15
Great Mathematicians, Great Mathematics

2013/14
Applying Modern Mathematics

2012/13
Shaping Modern Mathematics

All of Professor Flood's past Gresham lectures can be accessed here.